{"title":"Kudō-continuity of conditional entropies","authors":"M. Björklund, Yair Hartman, Hanna Oppelmayer","doi":"10.1214/22-aihp1313","DOIUrl":null,"url":null,"abstract":". In this paper we introduce the notion of Kudo-continuity for real-valued functions on the space of all complete sub- σ -algebras of a standard probability space. This is an a priori strengthening of continuity with respect to strong convergence. We show that conditional entropies are Kudo-continuous, and discuss an application to the study of Furstenberg entropy spectra of SAT*-spaces.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales de l Institut Henri Poincare D","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/22-aihp1313","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
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Abstract
. In this paper we introduce the notion of Kudo-continuity for real-valued functions on the space of all complete sub- σ -algebras of a standard probability space. This is an a priori strengthening of continuity with respect to strong convergence. We show that conditional entropies are Kudo-continuous, and discuss an application to the study of Furstenberg entropy spectra of SAT*-spaces.
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